Question: At the moment a certain medicine is injected, its concentration in the bloodstream is $120$ milligrams per liter. From that moment forward, the medicine's concentration drops by $30\%$ each hour. Write a function that gives the medicine's concentration in milligrams per liter, $C(t)$, $t$ hours after the medicine was injected. $C(t)=$
Dropping at a rate of $30\%$ per hour means the concentration keeps $100\%-30\%=70\%$ of its value each hour. So each hour, the concentration is multiplied by $70\%$, which is the same as a factor of $0.7$. If we start with the initial concentration, $120$ milligrams per liter, and keep multiplying by $0.7$, this function gives us the medicine's concentration $t$ hours after it was injected: $C(t)=120(0.7)^t$